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Transfer functions and cameras
Published in Neil Collings, Fourier Optics in Image Processing, 2018
The transfer function approach is valid for an ideal isoplanatic optical system. This ideal system is one where the translation of an object point in the object plane produces a proportional translation of the image point in the image plane. The diffraction-limited OTF is the transfer function for an ideal imaging system which is free from aberrations. The shape of the diffraction-limited OTF as a function of frequency is determined by the limiting aperture of the system, for example, the circular frame of the lens. This has been calculated for both square and circular limiting apertures [90]. It decreases monotonically from a maximum at zero spatial frequency to zero at a cut-off frequency, which is equal to the reciprocal of the product of the f-number of the lens and the wavelength of the light. The f-number is the focal length of the lens divided by the lens aperture. Higher f-number lenses have lower cut-off frequencies.
Optics in Digital Still Cameras
Published in Junichi Nakamura, Image Sensors and Signal Processing for Digital Still Cameras, 2017
In reality, because this depends on the cross-sectional area of the light beams, the brightness of the lens (the image plane brightness) is inversely proportional to the square of this F-number. This means that the larger the F-number is, the less light passes through the lens and the darker it becomes as a result. The preceding equation also shows that the theoretical minimum (brightest) value for F is 0.5. In fact, the brightest photographic lens on the market has an F-number of around 1.0. This is due to issues around the correction of various aberrations, which are discussed later. The brightest lenses used in compact DSCs have an F-number of around 2.0. When the value of θ′ is very small, it can be approximated using the following equation in which the diameter of the incident light beams is taken as D. This equation is used in many books.
Basic Optical Systems and Simple Photographic Lenses
Published in Daniel Malacara-Hernández, Zacarías Malacara-Hernández, Handbook of OPTICAL DESIGN, 2017
Daniel Malacara-Hernández, Zacarías Malacara-Hernández
An interesting and important characteristic of imaging optical systems is the total number of picture elements it produces (pixels), which depends on the f-number and on the aperture diameter. Assuming a perfect optical system, the smaller the f-number, the smaller the image element (diffraction image) is, as described when studying diffraction. On the other hand, given an image element size, a large field contains more image elements than a smaller field. Hopkins (1988) pointed out that the maximum total number of elements in an image is approximately equal to the square of the Lagrange invariant Λ multiplied by 4/λ2. The angular radius θ of an image element is equal to the radius of the Airy disk () θ=1.22λ2Y,
On the behavior of inhaled fibers in a replica of the first airway bifurcation under steady flow conditions
Published in Aerosol Science and Technology, 2022
Frantisek Lizal, Matous Cabalka, Milan Maly, Jakub Elcner, Miloslav Belka, Elena Lizalova Sujanska, Arpad Farkas, Pavel Starha, Ondrej Pech, Ondrej Misik, Jan Jedelsky, Miroslav Jicha
The precise evaluation of length of fibers is limited by the depth of field. Fibers out of the optimal focus appear shorter. The depth of field is determined by the subject distance, the lens focal length, and the lens relative aperture. For the given camera sensor size (20,48 × 20,48 mm) and the required image spatial resolution (1,3 µm/pix), the depth of field can be controlled only by changing the lens aperture. However, reducing the lens aperture (increasing f-number) reduces the amount of collected light, which severely reduces the contrast of fibers in the image. Moreover, very small apertures are likely to produce diffraction and reduce image overall sharpness. The optical setup used here was a carefully chosen compromise between depth of field, image brightness and sharpness